给定一个整数N ,任务是使用正整数和负整数构造一个大小为N 2且不包括0的矩阵,以使矩阵的总和等于矩阵对角线的总和。
例子:
Input: N = 2
Output:
1 -2
2 4
Explanation:
Diagonal sum = (1 + 4) = 5
Matrix sum = (1 – 2 + 2 + 4) = 5
Input: N = 5
Output:
1 2 3 5 10
3 1 4 -9 1
-19 6 1 5 -8
4 -7 2 1 12
-17 1 1 1 1
Explanation:
Diagonal sum = (1 + 1 + 1 + 1 + 1) = 5
Matrix sum = 5
方法:
解决此问题的方法是遍历矩阵的所有索引,并在N个对角线位置打印一个正元素(例如y ),并在其余N个位置平均分配一个单值正负整数(例如x和-x ) 2 – N个职位。
下面是上述方法的实现:
C++
// C++ program to implement
// the above approach
#include
using namespace std;
// Function to construct matrix with
// diagonal sum equal to matrix sum
void constructmatrix(int N)
{
bool check = true;
for (int i = 0; i < N; i++) {
for (int j = 0; j < N; j++) {
// If diagonal position
if (i == j) {
cout << 1 << " ";
}
else if (check) {
// Positve element
cout << 2 << " ";
check = false;
}
else {
// Negative element
cout << -2 << " ";
check = true;
}
}
cout << endl;
}
}
// Driver Code
int main()
{
int N = 5;
constructmatrix(5);
return 0;
}
Java
// Java program to implement
// the above approach
public class Main {
// Function to construct matrix with
// diagonal sum equal to matrix sum
public static void constructmatrix(int N)
{
boolean check = true;
for (int i = 0; i < N; i++) {
for (int j = 0; j < N; j++) {
// If diagonal position
if (i == j) {
System.out.print("1 ");
}
else if (check) {
// Positve element
System.out.print("2 ");
check = false;
}
else {
// Negative element
System.out.print("-2 ");
check = true;
}
}
System.out.println();
}
}
// Driver Code
public static void main(String[] args)
{
int N = 5;
constructmatrix(5);
}
}
Python3
# Python3 program to implement
# the above approach
# Function to construct matrix with
# diagonal sum equal to matrix sum
def constructmatrix(N):
check = bool(True)
for i in range(N):
for j in range(N):
# If diagonal position
if (i == j):
print(1, end = " ")
elif (check):
# Positve element
print(2, end = " ")
check = bool(False)
else:
# Negative element
print(-2, end = " ")
check = bool(True)
print()
# Driver code
N = 5
constructmatrix(5)
# This code is contributed by divyeshrabadiya07
C#
// C# program to implement
// the above approach
using System;
class GFG{
// Function to construct matrix with
// diagonal sum equal to matrix sum
public static void constructmatrix(int N)
{
bool check = true;
for(int i = 0; i < N; i++)
{
for(int j = 0; j < N; j++)
{
// If diagonal position
if (i == j)
{
Console.Write("1 ");
}
else if (check)
{
// Positve element
Console.Write("2 ");
check = false;
}
else
{
// Negative element
Console.Write("-2 ");
check = true;
}
}
Console.WriteLine();
}
}
// Driver Code
static public void Main ()
{
int N = 5;
constructmatrix(N);
}
}
// This code is contributed by piyush3010
输出:
1 2 -2 2 -2
2 1 -2 2 -2
2 -2 1 2 -2
2 -2 2 1 -2
2 -2 2 -2 1
时间复杂度: O(N 2 )
辅助空间: O(1)